"Beyond Space" is the title of a science fiction story I wrote that appears in the anthology 'The Mountain of Long Eyes' (Strategic Books)
Forever is a long time, and after all stars have died in a few trillion years, hard to say what will happen, if anything

When the Big Bang was first discovered, it was thought it must be slowing down - the initial ‘blast’ would be slowed by the gravitational pull of all the mass in the universe... but, when they were able to determine the velocity of the expansion - they were surprised to find it was *speeding up*... They don’t know whats causing it; the effect is called ‘Dark Energy’ - Dark, as in unknown, and energy that’s accelerating the expansion.
With this discovery, it doesn’t look like the expansion will ever stop.

And, ‘beyond space’ doesn’t really matter to us - at least, not yet... we have no way to see “outside” our universe, if there is an outside...